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x + 2 Factoring quadratic trinomials means finding the binomial factors when given a product. The factors represent the length and width of the rectangle. You are given the product – quadratic trinomial! You need to find the factors!

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Check by doing FOIL in your head! All of the previous problems involving quadratic trinomials had a leading coefficient of 1. Multiply a times c to find the product. b in the bottom represents the sum –3 –2 –3 1 You know there will be an x in each factor!

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Today’s problems involve factoring quadratic trinomials when the leading coefficient isn’t 1 - this includes negative 1. To factor quadratic trinomials when the leading coefficient isn’t 1, you will use the X figure and then factor out the greatest monomial factor (aka greatest common factor).

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+ 2 Step 1 Use the X figure as you did when the leading coefficient was 1. Multiply a times c to find the product. b in the bottom represents the sum –10 –3 –5 2 ( )( ) Step 2 Take the coefficient “a” and the x from the ax 2 term and the numbers from the sides of your X figure and place them into two parentheses in the following manner. – 5 Step 3 Factor out the greatest monomial factor from each parentheses if you can. Step 4 Discard the factor/s you pull out after X figure. Step 5 Check using FOIL.

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+ 2 –10 –3 –5 2 ( )( ) – 5 Check using FOIL. after You must discard (X out) the GMF that is pulled out after using the X figure!

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Before you use the X figure, you must factor out any greatest monomial factor, if possible! DO NOT DISCARD THIS FACTOR! before You must keep the GMF that is pulled out before using the X figure!

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( )( ) Factor Check using FOIL. If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

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before Factor out a GMF before the X figure – you must keep it! after Factor out a GMF after the X figure – discard it (X it out)!

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–4 5 A polynomial that cannot be written as a product of two polynomials with integral coefficients is called a prime polynomial! Try this problems...

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( )( ) Example Check using FOIL. Can you factor out a greatest monomial factor? Factor ( )( ) Example Can you factor out a greatest monomial factor? If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

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Example 4 Can you factor out a greatest monomial factor? Factor ( )( ) Example Check using FOIL. Can you factor out a greatest monomial factor?

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2 -6 ( )( ) Example Check using FOIL. Can you factor out a greatest monomial factor? Factor (10x - 8)(10x - 35) Example Check using FOIL. Can you factor out a greatest monomial factor? Make an organized list of factors